Page:EB1911 - Volume 19.djvu/986

 of a person’s death (now “obituary”). An “obit” was also a service performed at a funeral or in commemoration of a dead person, particularly the founder or benefactor of a church, college or other institution, hence “obit-days,” “obit Sunday,” &c. A “post-obit” is a bond given as a security for the repayment of money lent upon the death of a person from whom the borrower has expectations (see ).

OBITER DICTUM, that which is said by the way or in passing (Lat. ob, by, and iter, road); specifically, in law, an opinion expressed by a judge incidentally in the course of a case, on a point of law not necessarily connected with the issue or not forming part of the grounds of the decision; such obiter dicta have no binding authority.

OBJECT and SUBJECT, in philosophy, the terms used to denote respectively the external world and consciousness. The term “object” (from Lat. ob, over against, and jacere, to throw) is used generally in philosophy for that in which an activity of the mind ends, or towards which it is directed. With these may be compared the ordinary uses of the term for “thing” simply, or for that after which one strives, or at which one aims. “Subject,” literally that which is “thrown under” (sub), is originally the material or content of a discussion or thought, but in philosophy is used for the thought or the thinking person. The relation between the thinking subject and the object thought is analogous to the grammatical antithesis of the same terms: the “subject” of a verb is the person or thing from which the action proceeds, while the “object,” direct or indirect, is the person or thing affected. The true relation between mind or thought (subject) and matter or extension (object) is the chief problem of philosophy, and may be investigated from various standpoints (see and ). It should be observed that the philosophical use of “subject” is precisely the opposite of the common use. In ordinary language the “subject” of discussion, of a poem, of a work of art, is that which the speaker, author or artist treats.

OBJECTIVE, or, the lens of any optical system which first receives the light from the object viewed; in a compound system the rays subsequently traverse the eye-piece. The theoretical investigations upon which the construction of an optical system having specified properties is based, are treated in the article, and, from another standpoint, in the article. Here we deal with the methods by which the theoretical deductions are employed by the practical optician. It should be noted that the mathematical calculations provide data which are really only approximations, and consequently it is often found that a system constructed on such data requires modification before it fulfils the practical requirements. For example, take the case of a photographic objective. Calculations of the paths of two extreme rays in the meridional section of an oblique pencil of large aperture may prove that the rays intersect on a plane containing the axial focus, but similar calculations of many other rays would be necessary before the mean point of intersection could be settled with sufficient exactness. Suppose, however, that the optician has accurately realized the results of the mathematician, he can then determine the divergence of the practical from the theoretical properties by measuring the positions and conformation of the most distinct or mean foci, and, if sufficiently acquainted with the theory of the construction, he can modify one or more curvatures or thicknesses and so attain to a closer agreement with the ideal. Theory and practice co-operate in the realization of an original system. The order is not always the same, but generally the mathematician, by notoriously laborious calculations, supplies data which are at first closely followed by the constructor and afterwards modified in accordance with experimental observations.

In addition to the problem of constructing an original system, the optician has to deal with the reproduction of a realized system in different sizes. Two questions then arise: (1) To what degree of accuracy the radii of curvature can, or should, be repeated, and (2) to what degree of uniformity the surfaces can, or should be figured. With regard to the first point there is no great difficulty in working the requisite iron or brass tools of any curvature to within an error of th% of the radius; male and female templets being used for very deep curves, and the spherometer for tools of longer radii (by appropriate grinding together, the radii are alterable at will within narrow, but sufficient, limits). The accuracy attained in the grinding, however, is open to very perceptible modification by the subsequent polishing and figuring processes. This is particularly undesirable in the case of deep curves and large apertures. A variation in a radius of curvature may occasion a little spherical aberration at the axial focus, but if the amount be small it may be neutralized by imparting to the lens a parabolic form or its opposite. Such an artifice is frequently adopted in correcting large telescope objectives.

With optical systems which transmit large pencils with considerable obliquity (such as wide angle photographic objectives) the curves are very deep, and a departure from the true radius which would be tolerated in a telescope cannot be permitted here. Such lenses are usually tested by means of a master curve worked in glass. The master curve is fitted to the experimental lens, and an inspection of the interference fringes shows the quality of the fit—whether it be perfect, or too shallow or too deep. The Workman then modifies his polisher or stroke in order to correct the divergence. Flat surfaces are tested similarly. This test by contact has been strongly advocated and has been regarded as sufficient to detect all irregularities of any moment. This claim, however, is not justified, for the test is not sensitive to errors sufficient in amount to render a telescope objective almost valueless; but such errors are easily discernible by other optical devices. In general, accuracy in the radii of curvature is of primary importance and trueness of figuring is of secondary importance in photographic objectives, while the reverse holds with telescopic objectives; in wide angle microscopic objectives these two conditions are of equal moment. Eye pieces do not require the same degree of accuracy either in the curvature or the figuring.

A rough idea of the exactitude to which the figuring of the finest telescope objectives must be carried out is readily deduced. If two slips of paper, bearing printed letters of an in. high be placed in almost exact alignment, one 31·2 in. from the eye and the other 39 in., and viewed in moderate daylight with the eye having a pupillary aperture of of an in., one set of the letters will be legible while the other is not. In this case the difference of convergence or refracting power exercised by the eye in transferring its focus from one slip to the other is or one quarter diopter. If an image on the retina is diopter out of focus, then each point of the object is represented by a circle of confusion 0·0004 in. or 2′ 45″ in angular measure in diameter, the focal length of the eye being assumed to be 0·5 in. and the pupillary aperture of an in. If the effective aperture of the pupil or the aperture of a pencil traversing the pupil be 1/𝑛th of this standard, the size of the disk of confusion will be the same (viz. 0·0004 in.) if the retinal image be n quarter diopters out of focus. In general, for a constant size of the circle of confusion or, in other words, the same amount of visual blurring, the apertures of the pencils traversing the pupil and the focussing errors (expressed in quarter diopters) vary inversely.

If a portion of a figured surface of a telescope objective differs in curvature from the major portion of the lens so as to form a circle of confusion on the retina of a diameter not less than 2′ 45″, it is clear that the lens is faulty, the image formed by the perfect portion being sharp and well defined, and that formed by the imperfect portion blurred to the extent above determined, and to a greater extent if we allow for the effect of diffraction in the formation of the image. For example, a protuberance 1 in. in diameter at the centre of an object glass of 12 in. aperture refracting to a separate focus would theoretically form a spurious disk of about 5 seconds diameter, which would subtend a diameter of 50 minutes at the retina under a power of 600.

Regarding 2′ 45″ as the maximum diameter of a geometric circle of confusion permissible in a telescopic object glass, we proceed to determine the heights of the protuberance or depression which causes it. If 𝑓 be the equivalent focal length of the eye-piece and F that of the objective (the back focal length in the case of the microscope), then the linear error at the focus of the eye-piece is 𝑓2, or, expressed as a variation of 1/F, (𝑓/F)2, (＝∆$1⁄F$). If a lens has one side plane and is worked to a mathematically sharp edge, its thickness 𝑡 at the centre is (approximately) A2/8𝑟, where A is the whole aperture and 𝑟 the radius; and if 𝑔 be the equivalent focal length and the refractive index, we may write 𝑟＝𝑔(−1) and obtain